L06

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L06

• Demand

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Review

• Model of choice
• parameters
• Example 1 Cobb Douglass

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Perfect Complements
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Perfect complements

• We know
• Focus on one good (x1)
• How the demand is affected by a change
• a) in own price
• b) in income
• c) in price of other commodity
• One variable at the time!

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Own-Price Changes

• We focus on good 1
• We hold p2 and m constant.
• We change p1
• The change represented by
• Price offer curve
• Demand curve

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Own-Price Change p1
Vary p11, p13, p14
Fix p21 and m12.
x2
Demand curvefor commodity 1
p1 price offer curve
p1
(5,7)
(2.5,3)
(3,3)
x1
x1
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Own-Price Changes

• The curve containing all the utility-maximizing
  bundles traced out as p1 changes, with p2 and m
  constant, is the p1- price offer curve.
• The plot of optimal choice of x1 against p1 is
  the demand curve for commodity 1.

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Own-Price Changes

• The curve containing all the utility-maximizing
  bundles traced out as p1 changes, with p2 and m
  constant, is the p1- price offer curve.
• The plot of optimal choice of x1 against p1 is
  the demand curve for commodity 1.

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Ordinary and Giffen goods
p1
x1
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Two examples

• We find price offer and demand curve for
• Cobb-Douglas preferences
• Perfect complements
• In both cases we keep fixed

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Cobb-Douglass example
Data ,
variable
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Perfect Complements
Data
, variable
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Summary

• Price offer curve
• - Cobb-Douglas flat line
• - Perfect Complements optimal proportion line
• Demand curve
• - Cobb-Douglas downward slopping
• - Perfect Complements downward slopping
• Conclusion both ordinary goods
• Preferences generating Giffen good?

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Giffen Good
Demand curve has a positively
sloped part
x2
p1 price offer curve
p1
Û
Good 1 isGiffen
x1
x1
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Income Changes

• We still focus on good 1
• We hold p1 and p2 constant.
• We change m
• The change represented by
• Income offer curve
• Engel curve

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Income Changes
Vary m12, m6, m4
Fix p11, p21
x2
Engel curvefor commodity 1
income offer curve
m
(5,7)
(3,3)
(2,2)
x1
x1
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Goods

• A good for which quantity demanded rises with
  income is called normal.
• (positive slope of Engel curve)
• A good for which quantity demanded falls as
  income increases is called income inferior.
• (negative slope of Engel curve)

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Two examples

• We find income offer and Engel curve for
• Cobb-Douglas preferences
• Perfect complements
• In both cases we assume

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Cobb-Douglass example
Data ,
variable
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Perfect Complements
Data
, variable
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Summary

• Income offer curve
• - Cobb-Douglas ray from origin
• - Perfect Complements optimal proportion line
• Engel curve
• - Cobb-Douglas upward slopping
• - Perfect Complements upward slopping
• Conclusion both normal goods
• Preferences generating inferior good textbook.

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Cross-Price Effects

• If an increase in p2
• increases demand for commodity 1 then commodity 1
  is a gross substitute for commodity 2.
• reduces demand for commodity 1 then commodity 1
  is a gross complement for commodity 2.

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Cobb Douglas example
Gross complements of substitutes?
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Perfect Complements example
Gross complements